A rail corridor is a collection of tracks and sidings connecting two rail terminal areas. An example of a rail corridor 8 is shown in FIG. 1, showing a single main track 10 and three sidings 20. The western end of the rail corridor is on the left side of FIG. 1 and the eastern end on the right.
Scheduling rail transportation on a rail corridor is particularly complex as compared to highway, water, or air transportation. Trains using a single track traveling in opposite directions (i.e., a meet) or trains traveling in the same direction (i.e., a pass) must meet in the vicinity of a siding so that one train can be sided to let the other pass. Alternatively, if there exists a double main line with crossover switches, one train can be switched to the second main line to allow the other train to pass. Also, when such meets or passes occur at a siding, the siding chosen must be long enough to accommodate the train to be sided, and the train to be sided must arrive at the siding and have sufficient time to pull onto the siding before the passing train arrives at the siding.
The railroad must earn revenue from its transportation operations, and some of this revenue is generally at risk if trains cannot deliver freight on time. The destination time of the trains must be managed insofar as possible to prevent late penalties incurred by the railroad. Therefore scheduling trains across a rail corridor involves arranging meets and passes as required for all trains, and while also meeting the schedule for each train so that they all arrive, on time, at the end of the corridor.
Commercially applied scheduling processes attempted to date have been based on paradigms which involve simulation with branch and bound techniques to find a conflict-free schedule. Since a branch and bound process must sort through many binary choices as it proceeds toward a solution, these techniques are slow, and do not take advantage of quantitative relationships that can be adduced from the scheduling context.
Additionally, the prior art technique search processes actually become more complex and take longer to arrive at a solution as the number of sidings in the rail corridor increases. This is due to the search algorithms that form the basis for these prior art techniques. More sidings requires the search algorithm to search through and consider more choices before arriving at an optimum solution. As will be shown below, the technique of the present invention overcomes this disadvantage. Since the present invention calculates a cost function where each siding represents a lower cost, having more sidings will make it easier for the algorithm to identify the optimal (i.e. minimal) cost.
One prior art technique uses quantitative information such as train speed, destination, and time of departure as discrete variables in an artificial intelligence based system. The artificial intelligence process involves rules that are used to search through the trial cases until the best case is found. In addition to the considerable time taken by an artificial intelligence system to optimize a solution, it is also known that a slight change to the initial conditions may produce a significantly different result. In any case, a slight change to the initial conditions will require a new and lengthy computation to find the optimum solution. A commercial product referred to as The Movement Planner, offered by GE-Harris Railway Electronics L.L.C. of Melbourne, Fla., implements such an artificial intelligence solution.
As can be seen, the total set of parameters for scheduling a corridor can be large, and of both discrete and continuous types. Generally, a cost function based on these parameters can be formulated, and then some method of search is executed that will reduce the cost and/or find a feasible schedule for the subject trains. But, the presence of discrete variables in the search space prevents or greatly complicates the application of any "hill-climbing" search processes based on the use of gradients